How is sigma notation used to evaluate a series?

John's room is shaped like a box. It has a flat ceiling that is a rectangle that is 14 feet long and 8 feet wide and the walls a

erastova [34]

Okay so John needs to buy 7.6 quarts of paint so he would spend 26.55 on paint.

Hope this helps:)

6 0

3 years ago

Read 2 more answers

Solve the following system of equations for a and for b:

viktelen [127]

Answer:

$a=3\\b=1$

Step-by-step explanation:

$9a+3b=30\\8a+4b=28$

Let's solve the second equation for a to later on replace it in the first equation.

$8a+4b=28\\8a=28-4b\\a=\frac{28-4b}{8}$

Now plug this into the first equation.

$9a+3b=30\\9(\frac{28-4b}{8})+3b=30$

Distribute the 9

$(\frac{252-36b}{8}) +3b=30$

Break down the fraction.

$\frac{252}{8}-\frac{36b}{8}+3b=30$

Simplify.

$\frac{63}{2}-\frac{9}{2}b+3b=30$

Subtract $\frac{63}{2}$

$-\frac{9}{2}b+3b=30-\frac{63}{2}$

Combine like terms.

$\frac{-9+2*3}{2}b=\frac{30*2-63}{2}$

$\frac{-9+6}{2}b=\frac{60-63}{2}$

$\frac{-3}{2}b=\frac{-3}{2}$

Muliply by the reciprocal or inverted fraction next to b.

$(-\frac{2}{3})(-\frac{3}{2}) b=-\frac{3}{2}(-\frac{2}{3})$

$b=1$

Now plug this value into any of the equations to find the value of a.

$8a+4b=28\\8a+4(1)=28\\8a+4=28\\8a=28-4\\8a=24\\a=\frac{24}{8}\\ a=3$

5 0

4 years ago

A manufacturer of t-shirts marks a shirt as "irregular" when it has defects such as crooked seams, stains, rips, or holes. A sma

MaRussiya [10]

Answer:

The test statistic value is 1.474.

Step-by-step explanation:

In this case we need to determine whether the plant is making a higher than expected number of irregular t-shirts.

If more than 8% of the t-shirts manufactured at a plant are classified as irregular, the manager has to do an investigation to try to find the source of the increased mistakes in the manufacturing process..

The hypothesis for this test can be defined as follows:

H₀: The proportion of irregular t-shirts is 8%, i.e. p = 0.08.

Hₐ: The proportion of irregular t-shirts is more than 8%, i.e. p > 0.08.

The information provided is:

n = 100

X = number of irregular t-shirts = 12

Compute the sample proportion as follows:

$\hat p=\frac{X}{n}=\frac{12}{100}=0.12$

Compute the test statistic as follows:

$t=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}$

$=\frac{0.12-0.08}{\sqrt{\frac{0.08(1-0.08)}{100}}}\\\\=1.47441\\\\\approx 1.474$

Thus, the test statistic value is 1.474.

4 0

3 years ago

Find the sum of the angle measures in the figure below

Mekhanik [1.2K]

Answer:

540°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 5, hence

sum = 180° × 3 = 540°

6 0

4 years ago

What is 8 6/15 rounded to the nearest whole number

Lesechka [4]

Answer:

8

Step-by-step explanation:

5 0

3 years ago